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HOW much will climate change end up costing the world? The estimates, not surprisingly, vary widely. The United Nations Framework Convention on Climate Change (UNFCCC) estimates between $49 billion and $171 billion annually. A team of researchers at the Grantham Institute for Climate Change at Imperial College London has published a report that says UNFCCC is underestimating by a factor of two or three. Between 1996 and 2005, they point out, the annual damages done by hurricanes, fires, and other extreme weather was already averaging more than $50 billion per year. Yet few governments are willing to spend even fractions of that on preventative maintenance. Look at widespread fiddling over climate change; or the neglect of the dams surrounding New Orleans in the years before Hurricane Katrina devastated the city.

So would people be prepared pay to avoid future disasters? And if so, how much? That is the question tackled by Robert Pindyck of MIT's Sloan School of Management and Neng Wang of Columbia University, in a recent paper, "The Economic and Policy Consequences of Catastrophes." It is not easy to calculate accurately the likelihood of disasters. Some, such as rising sea levels or nuclear weapons gone rogue, have few historical precedents on which to base estimates. So Messrs Pindyck and Wang chose instead to model how likely people think it is that a catastrophe will occur, and how much money they would be prepared to spend to prevent it. In their model, the hypothetical household had to decide both the likelihood of a potential catastrophe and its magnitude, since a high-risk disaster with little consequence would affect spending behaviour differently to a rare but devastating event.

The model has the disadvantage of being, like many economic models, theoretical. But it has the advantages of not requiring people to have perfect information about the future, and being applicable to any disaster—not just climate change, but flu epidemics or widespread warfare. (Mr Pindyck himself reports being particularly worried about nuclear terrorism.)

Sky-is-falling economic modelling, so to speak, is not new. Two decades ago a paper by Thomas Reitz, then of the University of Iowa, pointed out that equity owners, even while acting averse to risk, demand high rates of return in anticipation of an unlikely, but severe, crash. More recently Richard Posner, of the University of Chicago, has argued at length that governments should spend more to prevent disasters that will probably not happen, but would be awful if they did. Mr Posner's blogging partner, Gary Becker, an economist, estimated in May the worldwide willingness to pay to avoid another flu pandemic at about $200 billion, even assuming the probability of such a pandemic occurring at only 1% over the next 20 years.

Messrs Pindyck and Wang's study lends credence to previous work which maps not only the probability of a risk occurring, but also the expected damage should it occur. In their model, even when a hypothetical consumer estimates the risk of a disaster occurring is close to zero, he still estimates the scale of potential devastation to be between 26% and 32% of national capital stock, far greater than the effects of Hurricane Katrina or even the 2004 tsunami. To avoid such a disaster entirely, or reduce its impact, the households in the model would be willing to pay a permanent consumption tax of up to 15%, depending on the size of the reduction and the likelihood of catastrophe.

In theory, then, governments should be able to spend far less than 15% to minimise the danger of catastrophes without suffering (political) risk. Although not every potential disaster could be averted, such studies provide rationale for spending money on the most pressing issues: stockpiling flu vaccines, shoring up rotting infrastructure, and, yes, preparing for higher sea levels. Unfortunately, climate change is just one area where people fail to act as rationally as they do within economic models.

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